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The sum 1/2 10C0 -10C1 + 2 .10C2 - 2^2 ...

The sum ` 1/2 10C_0 -10C_1 + 2 .10C_2 - 2^2 10C_3 + ......+ 2^9 10C_(10)` is

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The sum (1)/(2)10C_(0)-10C_(1)+2.10C_(2)-2^(2)10C_(3)+......+2^(9)10C is

Observe the following statements : Statement - I : 1/2 . ""^10C_0 - ""^10C_1 + 2. ""^10C_2 - 2^2. ""^10C_3 + ……+ 2^9. ""^10C_10 = -1/2 Statement - II : ""^20C_1 - 2(""^20C_2) + 3.(""^20C_3)-…..-20.(""^20C_20) = 0 Then the false statements are :

Observe the following statements : Statement - I : 1/2 . ""^10C_0 - ""^10C_1 + 2. ""^10C_2 - 2^2. ""^10C_3 + ……+ 2^9. ""^10C_10 = -1/2 Statement - II : ""^20C_1 - 2(""^20C_2) + 3.(""^20C_3)-…..-20.(""^20C_20) = 0 Then the false statements are :

Find 1/2.""^10C_0 -""^10C_1 +2.""^10C_2 - 2^2.""^10C_3+…..+2^9. ""^10C_10 = ?

Evaluate : ""^10C_1 + ""^10C_2 + ""^10C_3 + …. + ""^10C_10

The value of (^21C_1-^10C_1)+(^21C_2-^10C_2)+....+(^21C_(10)-^10C_(10)) is

Evaluate : ""^10C_1+""^10C_2+""^10C_3...... ""^10C_10 .

The sum (1)/(2)""^(10)C_(0)-""^(10)C_(1)+2.""^(10)C_(2)-2^(2)*""^(10)C_(3)+ . . .+2^(9)*""^(10)C_(10) equals: